Magnetic coupled detector of dynamic gravitational force gradients

ABSTRACT

This is a detector wherein a dynamic mass quadrupole arrangement includes two parallel conducting energized coils capable of moving relative to each other. The arrangement is coupled to a dynamic gravitational force gradient having a characteristic frequency, the coupling occurring through a dynamic stressenergy-momentum tensor in the quadrupole arrangement. A bridgeservo amplifier electrodynamical circuit resonant at the characteristic frequency is coupled to the coils for providing an output signal.

United States Patent [191 V Weber [451 Mar .27, 1973 [s41 MAGNETICCOUPLED DETECTOR on 3,273,397 9/1966 Forward..,.. ..73/382 DYNAMICGRAVITATIONAL FORCE OTHER PUBLICATIONS GRADIENTS Joseph Weber, ChevyChase, Md.

[75] Inventor:

[73] Assignee: Hughes Aircraft Company, Culver City, Calif.

22 Filed: Jan. 31, 1969 1 21 Appl. No.: 795,538

[52] US. Cl ..73/382 [51] Int. Cl. "(301V 7/04 [58] Field of Search..73/382, 505, 67.2; 310/82, 3 10/ 8.4

[56] References Cited UNITED STATES PATENTS 2,712,753 7/1955 Campbell..73/67.2

3,044,290 7/1962 Rawding", ..73/67.2

3,091,708 5/1963 Harris ..310/8.2

[57] ABSTRACT This is a detector wherein a dynamic mass quadrupolearrangement includes two parallel conducting energized coils capable ofmoving relative to each other. The arrangement is coupled to a dynamicgravitational force gradient having a characteristic frequency, thecoupling occurring through a dynamic stress-energymomentum tensor in thequadrupole arrangement. A

bridge-servo amplifier electrodynamical circuit resonant at thecharacteristic frequency is coupled to the coils for providing an outputsignal.

1 Claim, 13 Drawing Figures PATENT Enmzvms SHEET 1!]? 6 PATENIEUHARZHSYS3,722,287

SHEET 20F 6 PATENTEDHARZTISB v 3,722,287

SHEET 5 OF 6 Z/I- 40M MAGNETIC COUPLED DETECTOR F DYNAMIC GRAVITATIONALFORCE GRADIENTS This invention is divided out of patent application Ser.No. 399,682, filed Sept. 28, 1964, entitled Dynamic Gravitational ForceGradient Transducer. I

Dynamic gravitational fields take many forms. One form is the timevarying portion of the Newtonian gravitational force gradient field ofan oscillating or rotating asymmetric mass. Another form is thegravitational radiation described by the Einstein theory of gravity(General Theory of Relativity) that is emitted by an accelerated massquadrupole. Still another form is the effective dynamic gravitationalforce gradient field that is created by the relative motion of adetecting instrument through the static gravitational force gradientfield of a mass.

The generation and detection of dynamic gravitational force gradients isof importance in technological and scientific areas. It is of greatimportance to technology to have an instrument that will detect andmeasure the Newtonian gravitational force gradient fields existingaround large ore bodies and oil-containing formations while beingoperated on a moving platform. It is of further importance to technologyto have generators of dynamic gravitational force gradient fields totest the detectors of the invention as well as sensitive inertialdevices such as low level accelerometers prior to their use in thefield. It is still of further interest to technology to have a method ofsignaling in and out of electromagnetically and acoustically isolatedenclosures. It is also of great scientific importance to study thegravitational radiation emitted by astronomical sources such as rotatingbinary stars and exploding stars and galaxies to determine the innerstructure of these bodies, their dynamic behavior and the radiationgeneration mechanisms. It is of further scientific importance to studythe dynamic gravitational fields surrounding an oscillating or rotatingasymmetric mass to investigate the validity of Newtons laws of gravityin the high frequency region.

Prior to the devices described in'the present invention, there existeddevices for the detection and measurement of the anomalies created bygeological formations. One instrument presently in use for measuringstatic gravitational gradients is the Eotvos torsion balance whichemploys two equal weights on wires of two different lengths connected bya horizontal beam and suspended by a torsion fiber so that it is free torotate in a horizontal plane about the fiber. The beam rotates only whena differential horizontal force acts on the weights, and this occurswhen the gravitational field is distorted so that the horizontalcomponent at one end is different from that at the other. A number ofmeasurements are taken with the beam at different azimuthal orientationsand the results are employed in equations which, when solved, provide aplurality of quantities which define the gradient and curvature. Thetorsion balance has only limited usefulness due to the length of timerequired to make measurements. This long measurement time is related tothe inability to separate the desired gravitational response due to thegeological formation of interest from the noise sources arising from theoperation of the balance and from the inherent noise of the instrumentitself. The use of an instrument with dynamic response characteristicssuch as the devices of the invention operated in a manner which createsa dynamic interaction between the instrument and the gravitationalfieldof the geological formations will create a dynamic instrumentresponse with frequency characteristics that allow the desired signal tobeseparated from the noise by frequency filtering techniques.

Prior to the devices described in the present invention, there did existdevices for the generation of dynamic gravitational fields. Such devicesare typically two equal masses connected by a rod and rotated abouttheir center of mass. A survey of such work was recently published by J.C. Cook, On Measuring the Phase Velocity of an Oscillating GravitationalField, J. Franklin Inst., 273, pp. 453 47l, (June 1962). However, due tothe strong centrifugal forces that are induced in these types of devicesby theirrotation, they have the disadvantage of being limited by thestrength of materials to relatively low rotation rates. And also,because of this strength limitation, the rotating devices of the'priorart are not capable of generating appreciable dynamic gravitationalfields in the higher frequency regions as are the devices of the presentinvention.

However, there did not exist in the prior art any adequate method formeasurement of the dynamic gravitational force gradient fields createdby sources of interest to the scientific community. There do existdevices for the measurement of the dynamic force fields created by theNewtonian gravitational attraction of rotating or oscillating asymmetricmasses. Such devices usually take the form of an oscillatory pendulum(see J. C. Cook, FIG. 2). These pendulum devices are force measuringdevices and as such are not only sensitive to the Newtoniangravitational force, but are also sensitive to the inertial forcescaused by rotations and vibrations. The field of interest in scientificwork is the gradient of the dynamic gravitational force field. Thegravitational radiation emitted by astronomicaL sources is of a forcegradient or tensor type (rather than of a force or vector type as iselectromagnetic radiation and therefore requires an instrument thatresponds to dynamic gravitational force gradients. The dynamic Newtoniangravitational fields surrounding an oscillatory or rotating asymmetricmass contain both force fields and force gradient fields, but the onlypart that can be unambiguously assigned to gravitational effects is thedynamic force gradient, and therefore an in strument that responds onlyto the force gradient and does not respond to the force itself isrequired in order to separate the desired gravitational signal from theinertial noises.

Also, prior to the devices described in the present invention, there didnot exist any adequate method for gravitational fields surrounding anoscillating or rotating asymmetric mass.

It is still another object of this invention to provide an instrumentfor the generation of dynamic gravitational force gradient fields.

Yet another object of the invention is to provide an instrument for thegeneration of gravitational radiation.

Still another object of the invention is the transmission of energy bymeans of dynamic gravitational interactions.

And another object of the invention is that of signaling by means ofdynamic gravitational interactions.

And yet another object of the invention is the signaling by means ofgravitational radiation.

These and other objectives are achieved by a dynamic gravitational forcegradient transducer according to the invention comprising a massquadrupole arrangement bilaterally coupled to a dynamic gravitationalforce gradient having a characteristic frequency. The mass quadrupolecoupling to the dynamic gravitational field occurs through one or morecomponents of the dynamic stress-energy-momentum tensor contained in themass quadrupole arrangement. Coupled to the mass quadrupole is anelectrical input-output means, that in conjunction with the componentscomprising the dynamic stress-energy-momentum tensor, includes anelectrodynamical circuit which is resonant at a selected frequencycorresponding to the characteristic frequency of the dynamicgravitational force gradient. The electrical input-output meanspropagates therein energy corresponding to the magnitude and phase ofthe dynamic gravitational force gradient.

The invention and specific embodiments thereof will be describedhereinafter by way of example and with reference to the accompanyingdrawing, in which:

FIG. 1 is a perspective view ofa generator of dynamic gravitationalforce gradient fields constructed in accordance with the invention;

FIG. 2 is a perspective view of a detector of dynamic gravitationalforce gradient fields constructed in accordance with the invention andincluding a schematic representation of the electronic circuitry;

FIG. 3 illustrates schematically the interaction of a mass quadrupolewith gravitational radiation;

FIG. 4 is a schematic diagram of the coupling of two mass quadrupoles bydynamic gravitational fields;

FIG. 5 is a perspective view of an acoustically'resonant generatoraccording to another embodiment of the invention;

FIG. 6 is a perspective view of a particular form of the drivingelements used in the generator of FIG. 5;

FIG. 7 is a schematic diagram of a microwave frequency type detector ofdynamic gravitational force gradient fields in accordance with a furtherembodiment of the invention; j I

FIG. 8 is a perspective view of the transducer portion of the detectorof FIG.-7 or alternatively of a generator of microwave frequency dynamicgravitational force gradient fields;

a FIG. 9 is a perspective view of a magnetically levitatedsuperconducting type detector according to a still further embodiment ofthe invention;

FIG'. 10 is a sectional view of a piezoelectric transducer in accordancewith yet a further embodiment of the invention; 1

FIG. 11 is a sectional view of an electromagnetic transducer inaccordance with still another embodiment of the invention;

FIG. 12 is a schematic diagram of an electrostatically coupled massquadrupole containing a servo loop circuit in accordance with yetanother embodiment of the invention; and

FIG. 13 is a schematic diagram of a magnetically coupled mass quadrupolesimilar in construction to FIG. 12.

The generation and detection of dynamic gravitational force gradientfields and the signaling between 1 two such devices by means of dynamicgravitational fields is accomplished in accordance with the presentinvention by following the concept that any mass quadrupole containingnongravitational energy storage mechanisms will act as a transducer toconvert dynamic gravitational energy into some other form of energy.Usually the energy storage mechanism will be in the form of a resonantelectrodynamical circuit including a dynamic stress-energy-momentumtensor. For optimum coupling between the mass quadrupole and the dynamicgravitational force gradient field, the frequency of the resonantcircuit and the dynamic gravitational field must be the same and theorientation of the mass quadrupole and the gravitational field chosenproperly.

The dynamic stress-energy-momentum tensor as used here is meant todescribed the various forms of matter and energy that interact withdynamic gravitational fields, either to be a source of a dynamicgravitational field or to react to the forces exerted by thegravitational fields generated by other sources. These forms ofgravitationally active matter includes, for example, not only theordinary physical masses that are used in the usualdiscussion ofgravitational interactions that assume only the simplest version ofNewtons law of gravity, but also the energy and momentum associated withelectric and magnetic fields and electromagnetic radiation, the energyand momentum associated with mechanical stresses in material bodies.

and the electromechanical or magnetomechanical stresses that can be setup in electrically or magnetically active material bodies in intimateinteraction with electric or magnetic fields. A well-known example ofthis is the .combined interactions of magnetic fields and conductingfluids in the field of magnetohydrodynamics. Other forms of thestress-energy-momentum tensor are also possible, such as pressure, andthe dynamic forms of all of these can be utilized to generate and detectdynamic gravitational fields in the spirit of the invention.

Any mass quadrupole by definition has mass, so therefore, it contains atleast one component of the stress-energy-momentum tensor in the form ofmass so that it can interact with gravitational fields. One example ofthis is the gravitational force field. Since it is a mass quadrupolehowever, it can also interact with the gradient of the gravitationalforce field. (A single mass point also has a mass and also interactswith gravitational force fields, but not with the gradient of thegravitational force field.) In addition to the mass component of thestress-energy-momentum tensor in the mass quadrupole however, thereusually exists other forms as well, such as electromagnetic fields ormechanical stresses that may be just as effective or even more effectivethan the masses proper in the interaction with dynamic gravitationaiforce gradients.

An electrodynamical circuit is defined here as any combination of thevarious forms of the stress-energymomentum tensor with one or moreelectric, magnetic or mechanical storage elements or active electroniccircuits which act as storage elements, and an electrical input-outputmeans. For one example, the electrodynamical circuit could be oneconsisting entirely of electromagnetic fields, moving charges andalternating currents such as an electromagnetic cavity filled withionized gas where the electrons are driven by electromagnetic fields setup by alternating currents in a probe inserted into the cavity. Foranother example, the electrodynamical circuit could be anelectromechanical circuit consisting of accelerated massesinterconnected by mechanical vibrations and coupled to an electricalamplifier by a piezoelectric transducer. For yet another example, theelectrodynamical circuit could be a Beams type magnetic suspensionconsisting of two iron masses, one passive and the other active with therelative position of the two masses maintained by a servoamplifiercircuit with the error voltage monitored as the output signal.

In other words, the definition of electrodynamical circuit is to meaneither an electromechanical circuit or a servoamplifier circuit or adynamic electronic circuit.

Now, if it is wished to have control over the interaction of the massquadrupole with the dynamic gravitational force gradient fields, a waymust be found to couple to the dynamic stress-energy-momentum tensorwith the various types of electronic apparatus in order to form anelectrodynamical circuit. For those forms of a mass quadrupole thatcontain an electric or magnetic or electromagnetic form of the dynamicstress-energymomentum tensor, it is relatively easy to couple a wire toa voltage point, a loop around a current point or a waveguide to an irisin a cavity and insert or extract electrical energy. For those forms ofa mass quadrupole that contain mechanical vibrations, it has been foundthat it is easier to couple to the vibrations of the vibrating system byinteracting with the strains at the nodes rather than the more commonand obvious method of interacting with the motions at the antinodes.However, it may in certain instances be advantageous to couple to themotions at the antinodes. This may be accomplished by the conventionaluse of capacitive, inductive and magnetostrictive devices.

To couple to these strains, strain transducers (which do not interactwith motion directly) may be attached at the nodes where the strains area maximum. Piezoelectric crystals have been found to be satisfactorystrain transducers. By proper design and choice of crystal type, crystalorientation and electrical connections, the strain energy isconvertedinto electrical energy and vice versa by means of these transducers.These techniques are well known in the field of acoustics and can befound in references such as Piezoelectric Crystals and Their Applicationto Ultrasonics by Warren P. Mason, D. Van Nostrand Co.,

Princeton, N..I. (l959).

With reference to the drawings and more particularly to FIG. 1, there isshown an exemplary embodiment of a dynamic gravitational force gradienttransducer in the form of a generator of dynamic gravitational fields11. The generator 11 includes a transducer portion 12, comprising a pairof relatively heavy masses such as steel blocks 13 symmetricallysupported by a horizontally disposed elongated steel rod 15 which is inturn supported by a vertical steel rod 17 attached to a lower supportmember 19. Also, there is disposed symmetrically about the rod 15between the blocks 13 four elongated quartz rods 21 which are silverplated in such a manner that there is formed two insulated and nearlyhalf-cylindrical electrodes (not shown) along the length of each of thequartz rods 21. One of these electrodes of each of said quartz rods 21'is connected to 'a wire 23 which is in turn connected to a first outputterminal 25 of a source of signal energy such as the generator 27 whichin this case is a conventional amplitude type modulator normally used inmodulating amplitude modulated class C radiotelephone transmittingequipment. The other of the electrodes of each of said quartz rods 21 isconnected by conductive wire 29 to the second output terminal 31 of thegenerator 27 through a switch 33.

The generator 27 generates an AC output signal voltage at the frequencyof resonance of the transducer portion 12 of the generator 11. Thesignal is carried by the wires 23 and 29 when the switch 33 is in itsclosed position to the quartz rods 21 through the half-cylindricalelectrodes plated on these rods. The AC voltage, when applied to thequartz rods 21, causes a uniform strain throughout each of the rods 21which causes forces to be applied to the blocks 13 by the rods 21.

These forces set the blocks 13 in motion so that the blocks nowconstitute an accelerated mass quadrupole which quadrupole generatesdynamic gravitational fields.

Referring now to FIG. 2, there is shown a detector of dynamicgravitational force gradients 41. As can be seen by comparing FIGS. 1and 2, the mechanical structures areidentical but the electroniccircuitry is quite different. Accordingly, like reference numeralsdenote like components in these and all other figures.

In place of the generator 27, the wire 23 here connects to one terminalof a parallel inductor 43-capacitor 45 tuned circuit combination and toan input grid electrode 47 of a first electrometer vacuum tube 49 whichcomponents make up part of an input circuit to a low noise preamplifier51. The values for the inductor 43-capacitor 45 tuned circuit are chosento resonate at the frequency of resonance of the transducer portion 12.The wire 29 is here connected to the other terminal of the parallelinductor 43-capacitor 45 combination and to an input grid electrode 53of a secondelectrometer tube 55 of the preamplifier S1. Proper filamentvoltage and operating bias for the tubes 49 and 55 are provided by adropping resistor 57 connected between a 42 volt source (not shown) of13+ voltage and common connected filament terminals 59 and 61 of thetubes 49 and 55, respectively, and by a parallel resistor 63-capacitor65 combination connected between the other filament terminals 67 and 69and a common ground return 71. A filament bypass capacitor 73 isconnected between the filaments of the tubes 49 and 55. The plate loadresistors 74A and 74B of the tubes 49 and 55 are connected between theanode terminals 7S and 77, respectively, and the B+ terminal. Any signalpresent at the input circuit of the preamplifier 51 will be amplifiedand provided between output terminals 79 and 81 connected, respectively,to the anodes 75 and 77 of the tubes 49 and 55 through couplingcapacitors 83 and 85. The value of the various components of thepreamplifier 51 is given in the following table:

49 Type 5886 electrometer tube 55 Type 5886 electrometer tube 57 2,000ohm 1/2 watt 5% carbon resistor 63 1 50 ohm 1/2 watt 5% carbon resistor65 20 mf 50 volt capacitor 73 50 mf volt capacitor 74A 75 ,000 ohm 1watt 5% carbon resistor 748 75,000 ohm 1 watt 5% carbon resistor 83 0.1mf capacitor 85 0.1 mf capacitor When a dynamic gravitational forcegradient field is intercepted by the transducer portion 12 of thedetector 41, relative accelerations are produced between the blocks 13in such a manner to cause uniform strain in each of the quartz rods 21.The strain is uniform in the rods 21 because the mass of the blocks 13is much larger than the mass of the rods 21. By principles well known inthe electronic art, mechanical strain on a piezoelectric material suchas the quartz rods 21 cause the generation of electrical voltages at theopposite surfaces of the piezoelectric material. These voltages causedby the aforementioned uniform strain are con ducted to a balanced lownoise preamplifier circuit 51 by the conducting wires 23 and 29. Thepreamplifier 51 is adapted to amplify these voltages by a factor ofapproximately two to provide a relatively low noise output signalcorresponding to the magnitude and phase of the dynamic gravitationalforce gradient intercepted by the transducer portion 12. Furtheramplification of the output signal from the preamplifier 51 may beobtained by coupling a balanced high gain amplifier (not shown) to theoutput terminals 79 and 81 of the preamplifier 51.

In order to understand the method of operation of the devices of thepresent invention and to demonstrate that the interactions observed aredue to coupling of the devices to dynamic gravitational fields ratherthan some other interaction, a brief outline of the theory of dynamicgravitational interactions is here presented.

A dynamic gravitational field is defined as the time varying componentof the gravitational interaction between two structures which are inrelative motion. This is usually understood to mean that one of thebodies is undergoing oscillatory or translational motion in inertialspace and therefore its gravitational field varies with time. This timevarying gravitational field will then exert time varying forces on adetecting device.

There is also another possible methodfor a dynamic gravitationalinteraction in which the source body is stationary with respect toinertial space, and its gravitational field does not vary with time, butonly with position. If the detecting device is moving with respect toinertial space, then the spatially varying gravitational field of thesource is transformed, in the detecting bodys frame of reference, into atime varying gravitational field.

Mechanically, the two are nearly equivalent although the second type ofdynamic gravitational interaction is usually more practical.

It shall be assumed that all gravitational effects are correctlydescribed by Einsteins theory of gravity (General Theory of Relativity).(See for example A. Einstein, The Meaning of Relativity, fifth Edition,Princeton University Press, Princeton, New Jersey (1955); C. Moller, TheTheory of Relativity, Oxford University Press, London (1957); or J.Weber, General Relativity and Gravitational Waves, IntersciencePublications,

Inc., New York (1961).) It shall also be assumed that the cosmologicalconstant,sometimes included in the theory, is too small to be ofinterest in experimental work so that the field equations of generalrelativity will be assumed to have the form:

R at; /2g,,, R=(8'n'G/C T018 (1) where 0 3.00 X 10 m/sec is the speed oflight, G 6.67 X 10' m /kg sec is the Newtonian constant of gravity Tafiis the stress-energy-momentum tensor g g is the metric tensor describingthe properties of gravitation and space which is defined by the squareof the interval ds along the space-time world line s with the signaturechosen so that the flat space metric has the form:

R is the curvature scalar obtained from the contraction of the Riccitensor.

and R is the Ricci tensor obtained from the contraction of the Riemanntensor.

RUBZRX'YB The Riemann tensor or curvature tensor is defined in terms ofthe Christoffel symbols as:

and the Christoffel symbols are defined in terms of the metric tensor Itis assumed that the reader is familiar with tensor notation and theusual conventions such as automatic summation over repeated indices.

The Christoffel symbol defined in (7) is seen to be a convenientmathematical notation for a sum of products of the metric tensor and itsfirst derivatives.

Since the Riemann tensor (6) is defined in terms of sums and products ofthe Christoffel symbol and its first derivatives, it is seen to be aconvenient notation for a complicated combination of sums and productsof the metric tensor and its first and second derivatives. Since theRicci tensor and the curvature scalar (4) are sums of the products ofthe metric tensor and the Riemann tensor, this means that the left handsides of the field equations (1) comprise a very complicated, nonlinear,second order partial differential prescription for the calculation ofthe components of the metric tensor, given the distribution and behaviorof matter and energy in the form of the stress-energy-momentum tensor onthe right hand sides.

The usual process of calculating the dynamical behavior of a systemunder the influence of gravitational and other forces is quitecomplicated. First, all the mass and energy in both the system beinginvestigated and in the sources of the dynamic fields must bedetermined. Then, using these in a prescribed manner, the ten componentsof the stress-energymomentum tensor are calculated. Next, using thestressenergy-momentum tensor as the source term in the field equations(1), these ten nonlinear differential equations for the ten componentsof the metric tensor are solved. Then the metric tensor is used in thegeneralized equations of motion to determine how the system behaves.

For experimental purposes, it is not necessary to use the full fieldequations. The gravitational forces available are nearly always weakenough so that the nonlinear terms in the field equations arenegligible. Often the velocities involved are small enough so that evenspecial relativistic effects can be ignored. Thus, it is only necessaryto carry out the calculations using an appropriate approximation to thefull field equations.

To obtain a simplified form of the Einstein field equations that issuitable for experimental work, the weak field approximation will beused (see Weber, p. 87ff). This approximation uses the assumption thatthe gravitational potential energy in the gravitational fields involvedin an experiment is small compared to the kinetic energy and the restenergy of the masses and nongravitational fields used in the experiment.This assumption is satisfied to a very high degree of approximation byall conceivable experimental situations.

If the gravitational fields are weak, then the metric tensor can beapproximated by 808 z a aB where 8 is the flat space metric givenpreviously and the h g are the perturbations of the metric introduced bythe masses generating the gravitational fields. If the tensorgravitational potential is now defined as a certain combination of theperturbations h 5 on the flat space metric tensor and the necessarysubstitutions are made, we find that the nonlinear Einstein fieldequations become linear Poisson equations, or the weak field equations00' T =6 (13 F %85 F F 12 where the electromagnetic field tensor F (1Bis defined in terms of the electromagnetic four-potential Au as In orderto express the electromagnetic stress-energy-momentum tensor in terms ofthe more familiar electric and magnetic fields, it is necessary toseparate out the space-like components of the tensor from the time-likecomponents. The space-like components are just the components of thethree dimensional electromagnetic stress tensor ab a b a b ab( c c c c)while the time-like components are related to the momentum G, of theelectromagnetic waves and the energy density of the electromagneticfields.

o P'o (16) Since the electromagnetic fields have a stress-energymomentumtensor, and this tensor is the source of gravitational fields byEinsteins law of gravity, then a dynamic electromagnetic field cancouple to a dynamic gravitational field through the dynamicelectromagnetic stress-energy-momentum tensor.

The stress-energy-momentum tensor for physical matter is T p =[LC Ua U+S (17) where u is the density of the matter, SaB- is the elastic stresstensor of the material and Ua is the fourvelocity defined by la'x dt va=O 3' l 0 d7 611' c a=1. 3 (18) where v is the physical velocity. Thus,mechanical stresses can couple to gravitation through thestressenergy-momentum tensor. If the material is a fluid, then theelastic stress tensor degenerates into the scalar pressure Safi p andthe stress-energy-momentum tensor becomes to the stress-energy-momentumtensor. If the energy, and momentum in the stress or pressure fields canbeneglected in comparison to the rest mass energy and momentum of themasses involved, then the stressenergy-momentum tensor has thesimplified form T =uc U U 20 so that oscillating masses can couple todynamic gravitational fields through their contribution to thestress-energy-momentum tensor. Because gravitational experiments nearlyalways involve the use of physical masses with their large amounts ofconcentrated energy density, it is this final form of thestress-energy-momentum tensor that is usually used for calculations.However, under certain conditions and especially for high frequencyoperation, the electromagnetic and mechanical stress contributionsbecome as important as the mass motion contribution.

The simplest approximation to the weak field equations assumes that theonly sources of gravitational effects are physical masses'and that themasses involved not only have weak gravitational fields, but they alsohave low rotational rates or velocities compared with the speed oflight. In this approximation, the only component of thestress-energy-momentum tensor (20) that is not negligible is Since thevelocities are assumed to be low, the time derivatives of thegravitational potential are smaller than the spatial gradients of thepotential so the weak field equations (l 1) reduce to The equation forthe time-like component of the tensor gravitational potential (22) is athree dimensional Poisson equation which has the solution 00 I g V (23)This component of the tensor gravitational potential is easily seen tobe directly related to the scalar potential used in theNewtonian theoryof gravitation so that, as expected, the Einstein gravitational fieldequations reduce to the Newtonian gravitational field equation in thelowest approximation.

Normally, the interaction of the Newtonian gravitational field with adetecting mass is considered as a purely static one, but if the positionof the source mass (or the detecting mass) changes, then thegravitational field will vary with time and the interaction becomes adynamic one.

Besides the dynamic Newtonian interaction, there is also another dynamicinteraction governed by the Einstein law of gravity. This isgravitational radiation. The behavior of such radiation in anyphysically realizable experiment is governed by the weak fieldapproximation to the field equations, for as it stands, the weak fieldapproximation is a wave equation for the tensor gravitational potential(b t? The velocity of propagation is the same as the velocity of light.

The solution of the weak field wave equations with a nonvanishing sourceterm is well known as:

where r is the field point, r is the source point and R IF- F" l is thedistance from the source point to the field point.

The straightforward method of finding the solutions to these equationsis to calculate the kinetic and stress energy in the source and usethese directly. However, because of the laws of conservation of energyand momentum the various components of the stress-energymomentum tensorare not independent and it is possible to convert the integrals over thestresses into integrals over the more easily identified motional energyof the sources. When we do this, we see that the spatial components ofthe tensor gravitational potential depend upon the second timederivatives of the mass quadrupole moment of the source This equationshows that the lowest mode of gravitational radiation possible isquadrupole radiation. Thus, in general, any accelerated (i.e., rotatingor vibrating) mass quadrupole will emit gravitational radiation.

The fact that gravitational radiation is quadrupole can also beunderstood in terms of the law of conservation of momentum. In anysystem of particles, the momentum of these particles must be conserved.

m,)'c +m i +...=0 27 But the gravitational radiation that is possiblefrom these masses must come from the acceleration of the masses and ifthe equation for the conservation of momentum is differentiated, thenm,5c',+m 3i +...=0 (28) so that the gravitational radiation from eachpart of the source is cancelled (to first order) by the gravitationalradiation from some other part of the source. Thus, there is no dipolegravitational radiation, only quadrupole or higher multipole radiation.

The simplest quadrupole mass source for the calculation of gravitationalradiation energy emission is two equal masses rotating about theircenter of mass. This rotating type of source of gravitational radiationis the one normally considered in the prior art.

' The power radiated as gravitational radiation by these'rotating typesof systems can then be obtained from the well-known formula (see Weber,p. 97)

P=32GFm l5 C 29 where I 2ma is the moment of inertia of the source.Although this formula was derived for one specific case, it also appliesto any other linear system of masses. The only difference is thespecific form for the moment of inertia l.

From the exponents of F and a) in (29), it seems desirable, at firstglance, to work with a higher rotational speed, even if it means thatless mass could be used. However, it has been found that when thestrength of the material is considered, it is more advantageous to lowerthe rotational speed and to use a greater mass. Because of this strengthlimitation, the rotating devices of the prior art are very inefficientand are not capable of emitting appreciable amounts of gravitationalradiation, especially in the higher frequency regions. This, however, isnot true of such rotating astronomical sources such as binary starsystems since they are not held together by mechanical forces. Suchastronomical sources emit copious amounts of gravitational radiation andthis radiation can be detected by the devices of the invention.

Gravitational radiation can also arise from vibrational motion asdescribed in the devices of the present invention. The source of thegravitational field is the stress-energy-momentum tensor T c U,, U +Sso) which depends not only on the motion of the masses a, but also onthe elastic stresses S In a vibrating system, both the mass motion andthe elastic stresses are periodic and they both contribute to thegravitational radiation.

If it is assumed that acoustic resonance is present, then the power thatcan be emitted from a vibrating rod with a cross sectional area of A anda length of one half the acoustic wavelength is 'P= l61rGp Ave/l5 c (31)where v is the velocity of sound in the material, p is the density and eis the strain atresonance.

Since for acoustic resonance the ratio of the velocity of sound tothevelocity of light v/c z is a limitation, it is sometimes better tosuppress the acoustic resonance vibrations and use the stress tensor.This can be done by using a piezoelectric crystal and stressing it withelectromagnetic energy. With the proper formation of electrodes andcavity structures, electromagnetic resonance can be obtainedindependently of acoustic resonance. A single large crystal, driven inthis manner, will then give volume-integrated stress components whichare very large. The radiated gravitational power would then be P=1r GTM/l c 32 where T is the maximum tensile strength (about 2 X 10'newtons/m), and A is the gravitational wavelength. In this case, sinceelectromagnetic resonance is being used and not acoustic resonance, thewavelength is approximately twice the dimensions of thepiezoelectrically filled electromagnetic cavity (depending upon thedielectric constant of the material). This vibrational method ofgenerating high frequency gravitational radiation is orders of magnitudemore efficient than the rotating devices of the prior art.

Gravitational radiation can be thought of either as a propagatinggravitational field or the propagation of the curvature of space-time.This radiation, be it space curvature or gravitational field, will exertforces on objects with mass. Since gravitational radiation and alldynamic gravitational interactions are of quadrupole nature because ofthe conservation of momentum, it is necessary to use at least a massquadrupole to. interact with the radiation in order to detect itsexistence.

A mass quadrupole, by its very nature, involves a length. It is notdefined at a point but exists over a region about some point inspace-time. Since the masses or mass density making up the quadrupolemust be at different points in space-time, they each follow their ownseparate equation of motion along their own world line. Then, if thereare any gradients in the gravitational field or space curvature due togravitational radiation, the pathsof the two parts of the massquadrupole will differ slightly, indicating the presence of theradiation.

Conceivably, the two particles necessary for the mass quadrupolecould bein free fall (connected only by their gravitational attraction), thenthe passage of gravitational radiation would cause relative motionbetweenthe two particles. But then there are difficulties as to whetherthe particles would-be able to extract energy from the radiation orwhether they would just return to rest after the passage of theradiation.

If, however, the two parts of the mass quadrupole are coupled with anenergy converting mechanism that transforms the stress energy introducedby the gravitational radiation into some other form of energy such asacoustic vibrations or thermal energy, then the energy, once convertedby these irreversible processes, cannot be completely reconverted again.into gravitational energy. Thus, the radiation can be detected byextracting some of the energy out of the wave using a mass quadrupoleand an energy conversion mechanism.

There still might be some doubt as to whether the stresses due to thegravitational radiation are real and can exert strains in a materialbody. For example, the special relativistic contraction due to highrelative motion is not a physical effect that can be sensed by therapidly moving object, and it might be argued that because of theprinciple of equivalence between gravitational fields and coordinatesystems a similar effect would happen with gravitational radiation.However, the principle of equivalence is only valid at a point, and amass quadrupole does not operate over a point, so that although theacceleration of the center of mass of the mass quadrupole cannot beobserved, the gradient of the acceleration can be observed by therelative acceleration of the two masses of the mass quadrupole. Thereality of the tides is an excellent example: they are purelygravitational in nature, but the coordinate system that nature choosesto use for the motion of the earth has only found away to remove thecenter of mass forces and has not found a way to compensate for thedynamic gradient forces; they are real and energy can and is beingextracted from them.

If a mass quadrupole is used for the detection of gravitationalradiation, then there is present two particles, each with its ownequation of motion, and coupled together by their mutualnongravitational forces. The behavior of such a system is described bythe equation of differential motion (see Weber, p. l24ff) 0M IDs 5 7 U Un D/Dw (F /mc )dw=f /mc (33) where U is the four velocity, F is thenongravitational forces coupling the two parts of the mass quadrupoleand D/Ds is the covarient derivative with respect to the time. s, n isthe spatial displacement ofthe mass points, f is the force differencedue to the spatial gradient of the force DF /Dw operating across thedifferential distance dw, and By is the Riemann curvature tensor.

The use of this equation may be examined for the very simple massquadrupole detector consisting of two masses, each of mass m and aspring (see FIG. 3). The two world lines s of interest are those throughthe centers of two identical masses 101 and the distance n between thetwo world lines consists of the initiallength r of a spring 102 whichdoes not vary with time" and a small time varying extension 5 Thenongravitational forces connecting the two masses 101 consists of arestoring spring force k plus dissipation d due to the motion of thespring 102.

=km, 5 +cd (D I (as) In the limit of small, nonrelativistic vibrationsof a freely falling detector, the equation of differential motionbecomes:

This is the equation for a damped harmonic oscillator driven by certaincomponents of the Riemann tensor. Thus, by measurement of thedisplacement amplitude of a mechanical oscillator such as those of thepresent invention, the time varying space curvature induced bygravitational radiation can be calculated.

The previous description of the operation of the devices of the presentinvention in terms of the Einstein theory of gravity is informative andimportant in terms of the utilization of the devices in communication bygravitational radiation since only the Einstein theory can adequatelydiscuss the radiation aspects of gravitation However, for a detailedquantitafi ve discussion of the operation of the devices of theinvention, it is only necessary to assume a very simplified model thatis completely describable by the Newton law of gravity.

The dynamic gravitational interaction of two oscillating massquadrupoles may be investigated and are shown in FIG. 4. Each massquadrupole 151, 153 consists of two masses 155 and 157 having a mass ofm connected by spring 159 and 161, respectively, of nominal length 21,spring constant k, and damping constant D constrained to move only alongthe axis 162 and 163 through the two mass centers 165, 167. If it isassumed that the two mass quadrupoles 151, 153 are lying parallel toeach other, with separation d and one (the generator) is-being driven byan energy source (not shown) so that the masses 155, for example, areundergoing a periodic displacement acos wt, then the gravitational fieldof the generator will contain periodic variations. These periodicvariations of the gravitational field will cause periodic forces F andF, to be exerted on the two masses 157 of the second mass quadrupole(the detector) and will cause it to respond with a periodic motion withrelative amplitude g.

If Newtons law of reaction (F ma) is used for the masses, then thedifferential acceleration of the two masses 157 of the detector causedby the differential forces of the masses is given by En $11155 canal acos wt) (d a c05 wtw [d 21+ a cos wt) wherethe first term is due to thedifferential forces caused by the coupling F, of the detector masses 157to the nearest generator masses 155 and the second term is due to thedifferential forces caused by the coupling F between the detector masses157 and the furthest generator masses 155 (neglecting selfinteractions).

If l d is assumed, then after simplification there is obtained anequation If the mass m and spring constant k are chosen so that thedetector mass quadrupole 153 is resonant at the frequency w of thegenerator 151, and if the damping constant is expressed in terms of thefrequency w and energy storage factor Q, then the equation for thedetector becomes 2 5- (ax/Q) (Gma/Zd) cos (.5: 39)

where only the gravitational force gradient term that has a frequencycomponent at the frequency of resonance of the detector has been kept.

This is anequation for a damped harmonic oscillator and it has thesolution tions) I m=27rX 160 cps= 10 d= 1 foot.

With these experimental parameters, the strain predicted by theNewtonian laws of force and gravitation is There exist commercially,barium titanate dynamic strain transducers which have a voltage-straincharacteristic of 1.6 X 10 volts per unit strain. The voltage output ofsuch a transducer coupled to a strain of 10' in the mass quadrupoledetector is 1.6 microvolts. This is a voltage that is easily measured bystandard voltage measurement devices.

The above discussion shows that signals can be transmitted between twomass quadrupoles by dynamic gravitational interactions and demonstratesthat the devices of the invention couple to the dynamic gravitationalfields in a practical and usable manner, which is completely describablein terms of the well-verified Newtonian laws of gravity as well as theEinstein theory of gravity, and shows that the observed coupling is dueto dynamic gravitational interactions and not due to acoustic couplingor other extraneous factors.

Another embodiment of a dynamic gravitational force gradient fieldgenerator is shown in FIG. 5. An aluminum cylinder 21 1 is provided withfour piezoelectric strain transducers 213 (see FIG. 6) which are drivenby alternating electrical signals to generate strains in the cylinder211.

The aluminum cylinder 211, as shown in FIG. 5, represents a body ofelastic material with distributed mass including a mass quadrupole andis supported in the middle by a loop of wire 245. Because of its lowcost, ease of fabrication and high intrinsic Q, 6061 aluminum was usedas the cylinder 211 and operated in the first longitudinal vibrationalmode. The cylinder 211 was chosen to be 5 feet long and 8 inches indiameter with a first longitudinal mode frequency of 1,657

cps and with a shallow groove (not shown) for the wire 245. In order toprevent the coupling of the cylinder 211 to the surrounding air, thecylinder 211 is placed in a conventional vacuum chamber which is notillustrated for the sake of clarity. The chamber is maintained at anoncritical vacuum value of 500 microns or better.

To generate the strains produced within the cylinder 211, thepiezoelectric strain transducers 213 are attached to the cylinder 211 atthe nodes. For the first longitudinal mode, this node occurs at themiddle of the cylinder 211. The cylinder 211 is supported by the loop ofwire 245 at this nodal line. Since there is a minimum amount of motionat the nodal line, there will be a minimum amount of interaction withthe supporting loop of wire 245 and this will minimize the nonlinear ordissipative interactions that lower the Q. The odd higher orderlongitudinal modes also have a node at the middle of the cylinder 211 sothat by changing the frequency of the external electronics to include ormatch the frequency of these odd higher harmonics the cylinder 211 canbe used to generate dynamic gravitational force gradients at these otherfrequencies. The even order harmonics have an antinode at the middleposition so therefore their measured Q is substantially less than theodd order harmonics. If it is desired to operate at an even harmonic,two or more supporting loops of wire would have to be used 'and placedat the nodal points whose position would vary with the particular evenharmonic.

One of the transducers 213 is more clearly illustrated in FIG. 6. Thesetransducers are fabricated from barium titanate ceramic and areapproximately 6 inches wide, 8 inches long and 0.5 inches thick andcurved toto the coatings 247 and 248 of the transducer213 to facilitatelead connection.

In order that the electric output circuit (which includes among othersthe transducers 213 and the output impedance of the modulator) and themechanical vibrational resonant circuit of the cylinder 211 effectivelycombine to form an electromechanical circuit 18 with a single relativelyhigh Q resonance, it is necessary to use a sufficiently largenumber oftransducers 213 to provide a strong coupling. For the particularembodiment constructed and shown in FIG. 5, four such transducers wereused, althougha somewhat lesser number may provide good results.

With reference to FIGS. 7 and 8, there is shown a dynamic gravitationalforce gradient transducer embodiment incorporating a microwave cavitytype detector 401 which includes a rectangular microwave cavitystructure 403 coupled by means of a tapered transition section 405,consisting of a tapered waveguide section 406A and an inverse taperedfused quartz loading section 406B disposed therein to a firstrectangular waveguide section 407. The first waveguide section 407 is inturn connected to a first port 409 of a conventional microwavecirculator 411. The circulator 411 includes a second port 413 connectedto a second waveguide section 415 connected to a conventional maseramplifier 417. The circulator 411 also includes a third port 419 whichis connected to a third rectangular waveguide section 421. The waveguidesection 421 is in turn connected to a conventional microwave detector423 which is coupled by means of cable 425 to readout device which, inthis case, is a recorder 427.

The microwave cavity structure 403 (more clearly seen in FIG. 8)includes a coupling iris 431 disposed in a cavity end plate 433. Thecavity 403 is filled by a piezoelectric quartz crystal 435 in a mannerthat its xcut direction is parallel to the top and bottom portions 437and 439, respectively, of the cavity 403 and normal to an axis linethrough the coupling iris 431. An input signal, in the form of a dynamicgravitational force gradient having characteristic frequency, forexample, of 8 kmc upon impinging the crystal filled microwave cavity403, sets up dynamic volumetric strains in the quartz crystal 435. Thosedynamic strains along the active axis of x-cut quartz crystal 435 willcause the quartz to generate dynamic voltages through the piezoelectriceffect at top and bottom portions 437 and 439, respectively, of thecavity 403 which will vary at the frequency of the dynamic gravitationalfield. The dynamic voltages at these points of a microwave cavity excitemicrowaves in the cavity 403. The microwave cavity 403 is dimensioned tobe electromagnetically resonant at the frequency of the dynamicgravitational force gradient (8 kmc in this example) taking dueconsideration for the effect of the dimension of the iris 431 and theanistropic dielectric loading of the cavity 403 by the quartz crystal435. The Q of the cavity 403 will be determined by wall losses, thegeneration of acoustic waves in the quartz 435 by coupling back throughthe piezoelectric effect and by extraction of energy through thecoupling iris 431. The coupling iris 431 should be adjusted for bestmatch to the cavity in a manner well known in the microwave art. Thehighest Q is obtained for the cavity shown by using high quality quartzand lining the cavity with a superconducting material such as lead andcooling this material along with the maser 417 so as to obtain maximumcoupling to dynamic gravitational fields. A portion of the structuremicrowave energy is then coupled out through the iris 431, propagatedthrough the transition 405, the first waveguide section 407, thecirculator 413 and the second waveguide section 415 to the maseramplifier 417. The signal is then amplified by the low noise maser 417and is propagated through the second waveguide section 415, thecirculator 411 and the third waveguide section 421 to the microwavedetector 423. The output signal from the detector 423 is then coupled tothe recorder by means of cable 425. to indicate the magnitude and phaseduration of the input gravitational signal.

Alternatively, the microwave cavity structure 403 may be used as agenerator of dynamic gravitational fields by attaching the firstrectangular waveguide section 407 to a conventional source of microwaveenergy, such as a magnetron (not shown).- The microwave energy from themagnetron will travel back through the waveguide 407, through the iris431 and into the microwave cavity 403, there it will generatealternating electric and magnetic fields. The alternating electricfields will induce dynamic stresses in the quartz crystal 435 whichdynamic stresses will generate dynamic gravitational fields. When thetransducer is used as a generator, instead of the quartz crystal 435,there may be used other types of piezoelectric crystals or ceramics,electrostrictive liquids or solid materials, or magnetostrictivematerials.

With reference to FIG. 9, there is shown a dynamic gravitational forcegradient transducer embodiment 501 having three coils 503, 505 and 507,respectively, comprised of superconducting material such as lead orniobium. These coils are adapted to carry persistent currents of theorder of 1,000 ampere turns and are shown as having a single turn;however, they may comprise multi-turned coils. However, the coils mustform continuous loops which close upon themselves so that the currentremains constant in each of the coils. The current in each coil 503, 505and 507 then generates a magnetic field represented by the lines 8,, 8,,B respectively. The three coils 503, 505 and 507 are rigidly fixed to asupporting structure (not shown) which is constructed of anonsuperconducting material so that the coils 503, 505 and 507 areelectrically isolated from each other. The transducer 501 is cooled to atemperature below the transition temperature of the particularsuperconducting material used by placing the detector 501 is a liquidhelium bath (not shown) having temperature of approximately 4.2K,forexample. A first sphere 509 is symmetrically disposed between thefirst coil 503 and the second coil 505 and a second sphere 511 issymmetrically disposed between the second coil 505 and third coil 507.The spheres 509 and 511 comprise a mass quadrupole element. The spheres509 and 511 can consist, however, of either solid or hollow lead orniobium spheres or a lead plated plastic sphere, for example. Thus, whenintroduced into the cryogenic bath, the spheres 509 and 511 also becomesuperconducting and are levitated and contained between magnetic fields8,, B, and B generated by the coils 503, 505 and 507, respectively. Themethod of levitation of superconducting spheres by currents flowing insuperconducting coils is well known in the super conducting gyro art. Asto this point, reference may be made to an article authored by J. T.Harling and R. H Tuffias entitled The Cryogenic Gyro" in a book entitledAdvances in Cryogenic Engineering, K. D. Timmerhaus, editor, Vol. 6,Plenum Press, lnc., New York, l96l The coil to sphere diameter ratio ofapproximately two to one may be used with the coils 503, 505 and 507spacedapproximately one sphere diameter apartl For example, for theembodiment shown in FIG. 9, the radius of the coils 503, 505 and 507 maybe 4 cm, the radius of the spheres 509 and 511 equal to 2 cm and thecoils spaced 2 cm apart.

The magnetic field B of the center or second coil 505 acts as aspring-like coupling between the two masses 509 and 511. But thevelocity of propagation of the coupling is the velocity of light ratherthan the velocity of sound and therefore the cross section forgravitational radiation, which is indicative of sensitivity, isincreased substantially over that ofan acoustic type detector of thesame dimensions. A differential motion of the two spheres 509 and 511 ina direction along a symmetric axis through the centers of the spheres509, 511 due to interaction with a dynamic gravitational force gradientwill cause a time variation in the magnetic flux distribution in theregion between the spheres 509 and 511. This time varying magnetic fieldis sensed by a pick up coil 515 located either outside the coil 505 asshown in FIG. 9 or at the center of this coil. Alternately, the detector501 could be inserted in a superconducting container which hasdimensions chosen so that it acts as a microwave cavity resonant at thefrequency of vibration of the mass quadrupole magnetic suspensionsystem. Thus, the high frequency magnetic variations caused by thedifferential motion of the masses (spheres 509 and 511) create anelectromagnetic wave which will be stored in the microwave cavity. Theenergy so stored in the cavity can then be amplified and detected by alow noise microwave amplifier (maser, for example) and detectorarrangement.

With reference now to FIG. 10, there is shown a low frequency doublecavity type dynamic gravitational force gradient transducer 601consisting of a conductive double cavity structure 603 having a firstchamber 605 and second chamber 607. The first and second chambers 605and 607 have upper and lower walls 609, 611 and 613, 615, respectively.A first conductive electrode strip 617 is disposed within the firstchamber 605 and insulated from the upper wall 609 thereof by aninsulating member 619 which has an opening 621 communicating with asimilar opening 623 in the cavity structure 603. A conductive wire 625is coaxially disposed through the openings 621 and 623 and connected, bysoldering for example, to the first electrode 617.

Similarly, a second conductive electrode strip 627 is disposed withinthe second-chamber 607 and insulated from the lower wall 615 thereof byan insulating member 629 which has an opening 631 communicating with anopening 633 in the cavity structure 603. A conductive wire 635 iscoaxially disposed through the openings 631 and 633 and connected, bysoldering to the second electrode 627.

Also disposed in the cavity structure 603 is a first piezoelectriccrystal 637 attached (by a suitable adhesive) to the lower wall 611 ofthe chamber 605, and a second piezoelectric crystal 639 attached to theupper wall 613 of the chamber 607. The first and second crystals 637 and639 are so dimensioned that only the one fiat surface attached to thecavity structure 603 is in contact with this structure. The crystals 637and 639 are odd number of quarter wavelengths long at the frequency ofoscillation of the device.

Referring to FIG. 11, a coaxial cavity dynamic gravitational forcetransducer 651 is shown comprising a cylindrical cavity structure 653 ofa superconducting material wherein there is coaxially disposed asuperconducting center conductor 655 supported by a dielectric insulatedsupport member 657 of fused quartz or ceramic, for example. A couplingloop 659 is disposed within the structure 653 and adapted to cou ple outenergy propagating with the structure 653 in the form of electromagneticwaves. The transducer 651 is disposed in a liquid helium bath containedin a suitable cryogenic Dewar (not shown).

The detector 651 upon intercepting a dynamic gravitational forcegradient is able to sense the same because this dynamic gravitationalforce gradient field tends to alternately move the electrons in theupper and lower portions of the center conductor 655 in a differentialmanner so that there is no electron motion at the center of conductor655. This motion of electrons is in effect a current alternating at thefrequency of the dynamic gravitational force gradient. The currents thusproduced within the center conductor 655 in turn produce anelectromagnetic field within the cavity structure 653. The cavity 653 isso dimensioned that it is resonant at the aforementioned frequency andthis electromagnetic energy is coupled to a low noise amplifier circuit(not shown) by means of the coupling loop 659.

With reference to FIG. 12, there is shown a dynamic gravitational forcegradient detector 700 with a mass quadrupole element 701 consisting oftwo parallel conducting plates 703 and 705. These plates 703 and 705 arecoupled together by the electrostatic forces between them caused by thepositive voltage placed on the plate 703 by the bias battery 707 and thepositive or negative voltage placed on the plate 705 by a servoamplifier 709 through a conducting wire 711 and a conducting suspensionstrip 713. The conducting plate 703 is electrically connected to thebattery 707 by means of a second conducting suspension strip 715. Theconducting strips 713 and 715 are supported by an insulating member 717of dielectric material such as ceramic. If the plates 703 and 705, whichtogether make up a mass quadrupole 701, are acted upon by a dynamicgravitational force gradient, an increase in the relative spacingbetween the plates 703 and 705 will take place. This change in spacingcould also occur as a decrease in the distance between the plates.Accordingly, the capacitance of the plates 703 and 705 with respect toeach other will decrease or increase. As can be seen from FIG. 12, themass quadrupole 701 is coupled by means of capacitors 719 and 721 to oneleg of a conventional bridge circuit 723 wherein an oscillator 725 isconnected between opposite points of the bridge. Any change in thecapacitance between the plates 703 and 705 will thus cause an unbalancein the AC bridge circuit 723 driven by the oscillator 725 creating anunbalanced AC voltage between the opposite points 727 and 729 of thebridge circuit 723. This unbalanced voltage is detected by the phasesensitive servo amplifier 709 through error signal leads 735 and 737 andthe voltage is thus transformed into a substantially DC voltage whoseamplitude is proportional to the amplitude of the AC unbalanced voltageand whose polarity is dependent upon the phase of the AC unbalancedvoltage with respect to the phase reference signal obtained from thepoint 731 on the bridge circuit 723 through the phase reference lead739. The use and circuitry of such servo amplifiers as the servoamplifier 709 are well known in the art of control theory. The timeconstants of the'phase sensitive servo amplifier 709 are chosen so thatthe undamped natural frequency of the servo system is substantially thesame as that of the dynamic gravitational force gradient field and thedamping of the phase sensitive servo amplifier 709 is adjusted so thatthe servo amplifier 709 operates just below a point of oscillation. Withthese adjustments mentioned above, the electronic circuitry includingthe servo amplifier 709 acts as a resonant electrodynamical circuit witha frequency corresponding to the characteristic frequency of the dynamicgravitational force gradient and a high Q for maximum coupling to thedynamic gradient field.

FIG. 13 which in many respects is identical to that shown in FIG. 12shows a mass quadrupole element consisting of two self suspending coils751 and 753 which are coupled together by the magnetic forces betweenthem caused by current flowing through the loop 751 from the battery 707and a positive or negative current through the loop.753 from the servoamplifier 709. The function of the detector shown in FIG. 13 isidentical to the functioning of the detector of FIG. 12.

From the foregoing, it will be seen that there is described a dynamicgravitational force gradient transducer which may be used, for example,as a means of signaling through the use of dynamic gravitationalinteractions, and as an instrument for the detection of geologicalformations, and in many other described applications.

Although several specific embodiments have been herein illustrated, itwill be appreciated that other organizations of the specificarrangements shown may be made within the spirit and scope of theinvention. Additionally, other components or elements may be substitutedfor those which have been particularly named. For example, themechanical transducer portions of the devices can have torsionalvibrational resonant modes and/or a shear vibrational resonant modeswhich would be excited by the torques due to the dynamic gravitationalforce gradients. Furthermore, since every elastic body has a multitudeof mechanical vibrational resonant modes, each having a characteristicfrequency, then each mode can be coupled into a separate electricalcircuit having a corresponding resonant frequency to provide moreinformation on the frequency spectrum of the dynamic gravitational forcegradient field exciting the transducer. Also with reference to FIG. 10,the piezoelectric crystals 637 and 639 could alternatively beconstructed of alternate layers of quartz crystal and a dielectric witha thickness corresponding to one half an acoustic wavelength. Finally,it should be understood that the embodiments of the invention describedin the specification will function advantageously without elaboratemeans to reduce the noise factor but, of course, with reducedsensitivity.

Accordingly, it is intended that the foregoing disclosure and thedrawings shall be considered only as illustrations of the principles ofthis invention and are not to be construed in a limiting sense. i

What is claimed is: I

1. A dynamic gravitational force gradient detector, comprisingz-adynamic mass quadrupole arrangement including two' parallel conductingenergized coils resiliently mounted for resonant motion toward and awayfrom each other, said quadrupole arrangement

1. A dynamic gravitational force gradient detector, comprising: adynamic mass quadrupole arrangement including two parallel conductingenergized coils resiliently mounted for resonant motion toward and awayfrom each other, said quadrupole arrangement being coupled to a dynamicgravitational force gradient having a characteristic frequency equal theresonant motion of the plates said coupling occurring through a dynamicstress-energy-momentum tensor in said quadrupole arrangement; andelectrical output means connected to said coils and including abridge-servo amplifier electrodynamical circuit resonant at saidcharacteristic frequency for providing an output signal.